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Fan Wei

Fan Wei appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.COcond-mat.supr-coneess.SPMachine LearningComputer Visioncond-mat.quant-gasDiscrete MathematicsDistributed, Parallel, and Cluster ComputingInformation Theorymath.AGmath.ITmath.STStatistics Theory

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Published work

15 published item(s)

preprint2026arXiv

Transforming the Use of Earth Observation Data: Exascale Training of a Generative Compression Model with Historical Priors for up to 10,000x Data Reduction

Earth observation is becoming one of the largest data-producing activities in science, yet current pipelines still treat compression as a storage and transmission tool rather than a new way to use data. We present a generative compression framework that learns from historical Earth observation archives and enables on-demand 100x to 10,000x data reduction across downstream tasks. Unlike general visual data, Earth observation repeatedly measures the same evolving planet, making historical-prior learning feasible for extreme compression. To realize this paradigm, we train large generative compression models at exascale on the LineShine Armv9 CPU supercomputer, with co-optimization across model design, kernels, memory hierarchy, runtime, and parallelism. Our implementation sustains 1.54 EFLOP/s and peaks at 2.16 EFLOP/s in end-to-end training. This work shows that historical-prior generative compression can turn Earth observation data into an active, task-adaptive foundation for acquisition, delivery, storage, and scientific use.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Threshold Ramsey multiplicity for paths and even cycles

The Ramsey number $r(H)$ of a graph $H$ is the minimum integer $n$ such that any two-coloring of the edges of the complete graph $K_n$ contains a monochromatic copy of $H$. While this definition only asks for a single monochromatic copy of $H$, it is often the case that every two-edge-coloring of the complete graph on $r(H)$ vertices contains many monochromatic copies of $H$. The minimum number of such copies over all two-colorings of $K_{r(H)}$ will be referred to as the threshold Ramsey multiplicity of $H$. Addressing a problem of Harary and Prins, who were the first to systematically study this quantity, we show that there is a positive constant $c$ such that the threshold Ramsey multiplicity of a path or an even cycle on $k$ vertices is at least $(ck)^k$. This bound is tight up to the constant $c$. We prove a similar result for odd cycles in a companion paper.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Undecidability of polynomial inequalities in weighted graph homomorphism densities

Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate polynomial expressions in homomorphism densities on kernels $W$, i.e., symmetric, bounded, and measurable functions $W$ from $[0,1]^2 \to \mathbb{R}$. In 2011, Hatami and Norin proved a fundamental result that it is undecidable to determine the validity of polynomial inequalities in homomorphism densities for graphons (i.e., the case where the range of $W$ is $[0,1]$, which corresponds to unweighted graphs, or equivalently, to graphs with edge weights between $0$ and $1$). The corresponding problem for more general sets of kernels, e.g., for all kernels or for kernels with range $[-1,1]$, remains open. For any $a > 0$, we show undecidability of polynomial inequalities for any set of kernels which contains all kernels with range $\{0,a\}$. This result also answers a question raised by Lovász about finding computationally effective certificates for the validity of homomorphism density inequalities in kernels.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

On the inducibility problem for random Cayley graphs of abelian groups with a few deleted vertices

Given a $k$-vertex graph $H$ and an integer $n$, what are the $n$-vertex graphs with the maximum number of induced copies of $H$? This question is closely related to the inducibility problem introduced by Pippenger and Golumbic in 1975, which asks for the maximum possible fraction of $k$-vertex subsets of an $n$-vertex graph that induce a copy of $H$. Huang, Lee and the first author proved that for a random $k$-vertex graph $H$, almost surely the $n$-vertex graphs maximizing the number of induced copies of $H$ are the balanced iterated blow-ups of $H$. In this paper, we consider the case where the graph $H$ is obtained by deleting a small number of vertices from a random Cayley graph $\widetilde{H}$ of an abelian group. We prove that in this case, almost surely all $n$-vertex graphs maximizing the number of induced copies of $H$ are balanced iterated blow-ups of $\widetilde{H}$.

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preprint2020arXiv

Low Complexity Iterative Receiver Design for Sparse Code Multiple Access

Sparse code multiple access (SCMA) is one of the most promising methods among all the non-orthogonal multiple access techniques in the future 5G communication. Compared with some other non-orthogonal multiple access techniques such as low density signature (LDS), SCMA can achieve better performance due to the shaping gain of the SCMA codewords. However, despite of the sparsity of the codewords, the decoding complexity of the current message passing algorithm (MPA) utilized by SCMA is still prohibitively high. In this paper, by exploring the lattice structure of SCMA codewords, we propose a low complexity decoding algorithm based on list sphere decoding (LSD). The LSD avoids the exhaustive search for all possible hypotheses and only considers signal within a hypersphere. As LSD can be viewed a depth-first tree search algorithm, we further propose several methods to prune the redundancy visited nodes in order to reduce the size of the search tree. Simulation results show that the proposed algorithm can reduce the decoding complexity substantially while the performance loss compared with the existing algorithm is negligible.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Towrad 5G Air Interface Technology: Sparse Code Muliple Access

The fifth generation wireless networks focus on the design of low latency, high data rate, high reliability, and massive connectivity communications. Non-orthogonal multiple access (NOMA) is an essential enabling technology to accommodate the wide range of communication requirements. By coordinating the massive devices within the same resource block on power domain, frequency domain or code domain, NOMA is superior to conventional orthogonal multiple access in terms of the network connectivity, the throughputs of system and etc. Sparse code multiple access (SCMA) is a kind of multi-carrier code domain NOMA and has been studied extensively. The challenges for designing a high quality SCMA system is to seek the feasible encoding and decoding schemes to meet the desired requirements. In this article, we present some recent progresses towards the design of multi-dimensional codebooks, the practical low complexity decoder, as well as the Grant-Free multiple access for SCMA system. In particular, we show how the SCMA codebooks construction are motived by the combined design of multi-dimensional constellation and factor graphs. In addition, various low complexity SCMA decoders are also reviewed with a special focus on sphere decoding. Moreover, based on the framework of belief propagation, the SCMA Grant-Free transmission is introduced and the problem of collision resolution is also discussed.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A Self-Paced Regularization Framework for Multi-Label Learning

In this paper, we propose a novel multi-label learning framework, called Multi-Label Self-Paced Learning (MLSPL), in an attempt to incorporate the self-paced learning strategy into multi-label learning regime. In light of the benefits of adopting the easy-to-hard strategy proposed by self-paced learning, the devised MLSPL aims to learn multiple labels jointly by gradually including label learning tasks and instances into model training from the easy to the hard. We first introduce a self-paced function as a regularizer in the multi-label learning formulation, so as to simultaneously rank priorities of the label learning tasks and the instances in each learning iteration. Considering that different multi-label learning scenarios often need different self-paced schemes during optimization, we thus propose a general way to find the desired self-paced functions. Experimental results on three benchmark datasets suggest the state-of-the-art performance of our approach.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

On the number of cliques in graphs with a forbidden minor

Reed and Wood and independently Norine, Seymour, Thomas, and Wollan proved that for each positive integer $t$ there is a constant $c(t)$ such that every graph on $n$ vertices with no $K_t$-minor has at most $c(t)n$ cliques. Wood asked in 2007 if we can take $c(t) = c^t$ for some absolute constant $c$. This question was recently answered affirmatively by Lee and Oum. In this paper, we determine the exponential constant. We prove that every graph on $n$ vertices with no $K_t$-minor has at most $3^{2t/3+o(t)}n$ cliques. This bound is tight for $n \geq 4t/3$. More generally, let $H$ be a connected graph on $t$ vertices, and $x$ denote the size (i.e., the number edges) of the largest matching in the complement of $H$. We prove that every graph on $n$ vertices with no $H$-minor has at most $\max(3^{2t/3-x/3+o(t)}n,2^{t+o(t)}n)$ cliques, and this bound is tight for $n \geq \max (4t/3-2x/3,t)$ by a simple construction. Even more generally, we determine explicitly the exponential constant for the maximum number of cliques an $n$-vertex graph can have in a minor-closed family of graphs which is closed under disjoint union.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Dynamic Structure Embedded Online Multiple-Output Regression for Stream Data

Online multiple-output regression is an important machine learning technique for modeling, predicting, and compressing multi-dimensional correlated data streams. In this paper, we propose a novel online multiple-output regression method, called MORES, for stream data. MORES can \emph{dynamically} learn the structure of the coefficients change in each update step to facilitate the model's continuous refinement. We observe that limited expressive ability of the regression model, especially in the preliminary stage of online update, often leads to the variables in the residual errors being dependent. In light of this point, MORES intends to \emph{dynamically} learn and leverage the structure of the residual errors to improve the prediction accuracy. Moreover, we define three statistical variables to \emph{exactly} represent all the seen samples for \emph{incrementally} calculating prediction loss in each online update round, which can avoid loading all the training data into memory for updating model, and also effectively prevent drastic fluctuation of the model in the presence of noise. Furthermore, we introduce a forgetting factor to set different weights on samples so as to track the data streams' evolving characteristics quickly from the latest samples. Experiments on one synthetic dataset and three real-world datasets validate the effectiveness of the proposed method. In addition, the update speed of MORES is at least 2000 samples processed per second on the three real-world datasets, more than 15 times faster than the state-of-the-art online learning algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Quantum Phase diagram and time-of-flight absorption pictures of ultracold Bose system in a square optical superlattice

In this letter, by the use of the generalized effective potential theory, with the help of process-chain approach under the framework of Kato formulation of perturbation expansion, we calculate out the quantum phase diagram up to 8-th order for an ultracold Bose system in a square optical superlattice. Base on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are gotten, which are in excellent agreement with recent Monte-Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Involutions on standard Young tableaux and divisors on metric graphs

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the $v_0$-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Dvoretzky--Kiefer--Wolfowitz Inequalities for the Two-sample Case

The Dvoretzky--Kiefer--Wolfowitz (DKW) inequality says that if $F_n$ is an empirical distribution function for variables i.i.d.\ with a distribution function $F$, and $K_n$ is the Kolmogorov statistic $\sqrt{n}\sup_x|(F_n-F)(x)|$, then there is a finite constant $C$ such that for any $M>0$, $\Pr(K_n>M) \leq C\exp(-2M^2).$ Massart proved that one can take C=2 (DKWM inequality) which is sharp for $F$ continuous. We consider the analogous Kolmogorov--Smirnov statistic $KS_{m,n}$ for the two-sample case and show that for $m=n$, the DKW inequality holds with C=2 if and only if $n\geq 458$. For $n_0\leq n<458$ it holds for some $C>2$ depending on $n_0$. For $m\neq n$, the DKWM inequality fails for the three pairs $(m,n)$ with $1\leq m < n\leq 3$. We found by computer search that for $n\geq 4$, the DKWM inequality always holds for $1\leq m< n\leq 200$, and further that it holds for $n=2m$ with $101\leq m\leq 300$. We conjecture that the DKWM inequality holds for pairs $m\leq n$ with the $457+3 =460$ exceptions mentioned.

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preprint2010arXiv

Non-adiabatic effects of superconductor silane under high pressure

Investigations of non-adiabatic effects by including vertex corrections in the standard Eliashberg theory show that high phonon frequency is unfavorable to superconductivity in regime of strong vertex correction. This means that it is hard to find high-transition-temperature superconductors in the compounds with light elements if the non-adiabatic effects are strong. The interplay interaction between non-adiabatic effect and Coulomb interaction makes the transition temperature of silane superconductor not so high as predicted by the standard Eliashberg theory.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Tc map and superconductivity of simple metals at high pressure

We calculate Tc map in region of weak electron-phonon coupling based on simple phonon spectrum. By using linear-response method and density functional theory, we calculate phonon spectra and Eliashberg functions of simple metals under pressure. Based on the evolutions of superconducting parameters of simple metals on the Tc map with increasing pressure, we find that there are two different responses to pressure for simple metals: (1) enhancing electron-phonon interaction $λ$ such as for La and Li, (2) increasing phonon frequency such as for Pb, Pt. The $λ$ threshold effect is found, which origins from the competition between electron-phonon interaction and electron-electron Coulomb interaction and is the reason why Tc of most superconductors of simple metals are higher than 0.1K.

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preprint2010arXiv

The Weak Bruhat Order and Separable Permutations

In this paper we consider the rank generating function of a separable permutation $π$ in the weak Bruhat order on the two intervals $[\text{id}, π]$ and $[π, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising result that the product of these two generating functions is the generating function for the symmetric group with the weak order. We then obtain explicit formulas for the rank generating functions on $[\text{id}, π]$ and $[π, w_0]$, which leads to the rank-symmetry and unimodality of the two graded posets.

0 citations0 reviewsNo code linkedOpen access